JOURNAL of MULTISCALE NEUROSCIENCE

OIGINAL RESEARCH

We extend our previous paper on deriving an approximate analytical solution of a nonlinear cable equation by including other ion channels in neurons and calcium dynamics based on reaction-diffusion dynamics that lead to a system of nonlinear cable equations. Here, excitable dendrite possesses clusters of voltage-activated ion channels that are discretely distributed as point sources or hotspots of transmembrane current along a continuous cable structure of fixed length. Single and/or trains of action potentials and spatially distributed synaptic inputs drive the depolarisation and activate sparsely distributed voltage-dependent calcium channels. This leads to calcium influx and diffusion in the cable. Here, time-dependent analytical solutions were obtained by applying a perturbation expansion of the non-dimensional voltage (Φ) and non-dimensional calcium (ΦCa) and then solving the resulting set of integral equations. We use this framework to gain insights into calcium-driven synaptic plasticity in dendrites. Many previous studies have traditionally focused on the local impact of calcium on whether the synapse's strength is increased (potentiated) or decreased (depressed). Only recently have studies focusing on heterosynaptic plasticity been gaining popularity, and here we ask the question of how a local plasticity rule is influenced by the spatially and temporally distributed synaptic inputs. Specifically, we focus on how synaptic inputs and calcium influx impact a calcium-derived temporal learning window for spike-timing-dependent plasticity (STDP) at nearby sites to assess the nature of the resulting distance-dependent interaction on the associated learning window at the synapse of interest.

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Keywords:  Ion channels, Spike trains, Sparsely excitable dendrites, Integrative modelling, Ionic cable equation, Green's
functions, calcium-based synaptic plasticity, Spike timing-dependent plasticity (STDP).

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Conflict of Interest

The author declares that he was an editorial board member of JMN, at the time of submission. This had no impact on the peer review process and the final decision.

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This article belongs to the Special Issue                

Dynamic Multiscaling in Neuroscience

    Lead Editor:  Dr. Nicolangelo Iannella

         University of Oslo, Norway

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Copyright: © 2024 The Author(s). Published by Neural Press.

This is an open access article distributed under the terms and conditions of the CC BY 4.0 license.

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